function u_aver = get_average(A0_coef, basis,N)
weights = [8/9,5/9,5/9];
[row,col] = size(A0_coef);
k = row ;
u_aver = zeros(1,N);
for i = 1 : N
    value = basis(:,1:k)*A0_coef(:,i);
    u_aver(i) = (1/2)*(weights*value);
end
end